Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 27, 2017; final manuscript received January 4, 2018; published online February 9, 2018. Assoc. Editor: Mahmoud Hussein.

For practical applications of the elastic metamaterials, dynamic behavior of finite structures made of elastic metamaterials with frequency dependent properties are analyzed theoretically and numerically. First, based on a frequency-dependent mass density and Young's modulus of the effective continuum, the global dynamic response of a finite rod made of elastic metamaterials is studied. It is found that due to the variation of the effective density and Young's modulus, the natural frequency distribution of the finite structure is altered. Furthermore, based on the spectral approach, the general wave amplitude transfer function is derived before the final transmitted wave amplitude for the finite-layered metamaterial structure with decreasing density is obtained using the mathematical induction method. The analytical analysis and finite element solutions indicate that the increased transmission wave displacement amplitude and reduced stress amplitude can be controlled by the impedance mismatch of the adjacent layers of the layered structure.

Displacement comparison of the remote end in the effective continuum rod and metamaterial-based rod for (a) natural frequency distribution comparison and (b) natural frequency concentration in the first passing band

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